Nonabelian Algebraic Topology :
filtered spaces, crossed complexes, cubical homotopy groupoids by Ronald Brown,
Philip J. Higgins, Rafael Sivera (description
of new book: xxxv+668 pages, full pdf downloadable as hyperref
e-book; EMS Tract vol 15,
ISBN 978-3-13719-083-8, August 2011).
This gives a new foundation for algebraic
topology, relying on a Seifert-van Kampen Theorem for the fundamental
crossed complex of a filtered space, which allows new proofs of some classical
theorems such as the Relative Hurewicz Theorem; it also allows new calculations
of some nonabelian second relative homotopy
groups, not available by traditional methods of singular homology
and simplicial approximation. Indeed, it allows computation of some homotopy
2-types, based on calculations with crossed modules. Dealing with algebraic
models of homotopy types requires a different approach to algebraic topology
than the classical one.

DPhil Thesis: `Some problems in algebraic topology: a study of function space,
function complexes, and FD-complexes' Submitted December, 1961, 140 pages.
Complete thesis 154 pages The final Appendix was recalled from the exam and superceded
by my first two papers.

Other output

(i) ``How mathematics gets into knots'', London Mathematical Society Popular
Lectures Video Series, (1987) 50 min.
(ii) ``Mathematics and knots'', Exhibition of 16 A2 boards, designed by R.Brown,
N.D.Gilbert, and T.Porter, Mathematics and Knots, Bangor, 1989. Exhibited
at the Royal Society/ Joint Mathematical Council Pop Maths Roadshow, 1989-90;
British Association for the Advancement of Science, Swansea, 1990; National
Science Festival, Edinburgh, 1994.
(iii) ``Pivoted lines and the M\"obius Band'', Computer Graphics Video,
Storyline by R. Brown, Programming by Ramen Sen, Mathematics and Knots /
IBM UK 4min. (1992). See the end of Pivoted lines and the Möbius Band.
(iv) ``Symbolic Sculptures and Mathematics'',
Symbolic Sculptures and Mathematics
Sculptures: John Robinson. Production: Cara Quinton. Mathematics: Ronald
Brown. Edition Limitée; Centre for the Popularisation of Mathematics,
1996.
(v)Web Site
Knot Exhibition
Centre for the Popularisation of
Mathematics, 1997.
(vi) `Raising public awareness of mathematics': This was a CDRom published for World Mathematics Year 2000 and funded by the EC.
It is largely incorporated in this web site .

P2. (with C.D.WENSLEY), ``On sorting sequences''.
02.25 BROWN,
R. & HIGGINS, P.J.
The fundamental groupoid of the quotient of a Hausdorff space by a discontinuous
action of a discrete group is the orbit groupoid